Community detection in complex networks has attracted considerable attention, however, most existing methods need the number of communities to be specified beforehand. In this paper, a goodness-of-fit test based on the linear spectral statistic of the centered and rescaled adjacency matrix for the stochastic block model is proposed. We prove that the proposed test statistic converges in distribution to the standard Gaussian distribution under the null hypothesis. The proof uses some recent advances in generalized Wigner matrices. Simulations and real data examples show that our proposed test statistic performs well. This paper extends the work of Dong et al. [Information Science 512 (2020) 1360-1371].

翻译：复杂网络中的社区检测引起了人们极大的关注，然而，大多数现有方法需要事先指定社区数。本文提出了一种基于中心化和标准化邻接矩阵的线性谱统计的随机块模型拟合优度检验。我们证明了在零假设下，所提出的检验统计量收敛于标准高斯分布。证明过程使用了最近推出的广义Wigner矩阵理论。仿真和实际数据示例表明，所提出的检验统计量表现良好。本文扩展了Dong等人在[Information Science 512(2020)1360-1371]的工作。